Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Derivation of the Cable Equation

Description

This lecture covers the derivation of the cable equation in the context of computational neuroscience, focusing on modeling dendrites as cables and their behavior in response to synaptic inputs. The instructor discusses the mathematical formulation and implications of the cable equation, leading to an understanding of compartmental models and the role of active dendrites.

In MOOC

Neuronal Dynamics - Computational Neuroscience of Single Neurons

Official source

Related concepts (32)

Synapse

In the nervous system, a synapse is a structure that permits a neuron (or nerve cell) to pass an electrical or chemical signal to another neuron or to the target effector cell. Synapses are essential to the transmission of nervous impulses from one neuron to another. Neurons are specialized to pass signals to individual target cells, and synapses are the means by which they do so. At a synapse, the plasma membrane of the signal-passing neuron (the presynaptic neuron) comes into close apposition with the membrane of the target (postsynaptic) cell.

Chemical synapse

Chemical synapses are biological junctions through which neurons' signals can be sent to each other and to non-neuronal cells such as those in muscles or glands. Chemical synapses allow neurons to form circuits within the central nervous system. They are crucial to the biological computations that underlie perception and thought. They allow the nervous system to connect to and control other systems of the body. At a chemical synapse, one neuron releases neurotransmitter molecules into a small space (the synaptic cleft) that is adjacent to another neuron.

Dendrite

A dendrite (from Greek δένδρον déndron, "tree") or dendron is a branched protoplasmic extension of a nerve cell that propagates the electrochemical stimulation received from other neural cells to the cell body, or soma, of the neuron from which the dendrites project. Electrical stimulation is transmitted onto dendrites by upstream neurons (usually via their axons) via synapses which are located at various points throughout the dendritic tree.

Telegrapher's equations

The telegrapher's equations (or just telegraph equations) are a set of two coupled, linear equations that predict the voltage and current distributions on a linear electrical transmission line. The equations are important because they allow transmission lines to be analyzed using circuit theory. The equations and their solutions are applicable from 0 Hz to frequencies at which the transmission line structure can support higher order non-TEM modes. The equations can be expressed in both the time domain and the frequency domain.

Mathematical modelling of infectious diseases

Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc.

Related lectures (49)

Rall's Cable Model MOOC: Simulation Neurocience

Explores Rall's cable model, synaptic potential spread in dendrites, and compartmental modeling for neural simulations.

Introduction into the module MOOC: Simulation Neurocience

Introduces nerve cells' electrical activity, focusing on spikes and synaptic potentials.

Understanding Synaptic Transmission

Explores synaptic transmission, neurotransmitters, and neural plasticity principles.

Modeling the synaptic potential MOOC: Simulation Neurocience

Explores the modeling of synaptic potentials and the factors influencing their amplitude.

Synapses: Neuronal Dynamics MOOC: Neuronal Dynamics - Computational Neuroscience of Single Neurons